Monday, September 01, 2008

Can Mere Numbers Prove The Existence Of God?

Introduction: The following scene relates a discussion between a Christian math teacher and his student. The student had asked the teacher for evidence for the existence of God. The teacher, being a dutiful Christian and a budding apologist, decides to explain the concept of “numbers” to the student.

Act One, Scene 1

The teacher wrote the number 1 on the white board.

Teacher (T): What is the number I have just written on the board?

Student (S): Eh, I don’t really know what you are driving at, but I guess it is obvious even to my pet parrot that this is the number 1.

T: Are you sure that this is the number 1?

S: Why? Yes, I’m dead sure.

T: So if I rub away the number 1 from this board, the number 1 has ceased to exist?

S: I don’t understand you there.

T: You claimed that this is the number 1. So, if I were to use the cleaner and rub away this number 1, does the number 1 cease to exist?

S: Eh, no.

T: So this is not the number 1?

S: Eh, no. But I don’t know how to put it across to you.

T: You see, what is on the board is not the number 1. It is merely a reference to the number 1.

S: You mean that what you wrote on the board merely represents the number 1?

T: Yes. The number 1 is a concept, an abstract idea to be exact. Numbers cannot exist in the material or naturalistic plane of existence.

S: So where do numbers exist?

T: Isn’t it strange that many mathematicians never ask this question, “What really are numbers?” You see, numbers are ideas or concepts, and ideas or concepts can only exist in minds.

S: I am beginning to understand what you are driving at. You are telling me that numbers can exist in minds, and I presume “minds” include the minds of men or human beings.

T: That is correct. Numbers can be conceived by the minds of men, but not only by the minds of men. If there are other intelligent beings with minds, numbers can likewise exist or be conceived by such other minds.

S: Alright. So numbers are ideas, and they can only exist in minds. So where is the evidence for God?

T: Be patient, my friend. Numbers are not only ideas or concepts, but are also immutable ideas/concepts.

S: Immutable as in unchangeable? Why so?

T: Take the number 1 as an example. If number 1 changes in any manner i.e. quantitatively, it ceases to be 1. The concept of number 1 has to be absolutely unchanging, and what references to the number 1 we use in math (e.g. the number 1 we write on paper or key into the calculator) has to refer to the perfect form of the number 1. The number 1 we write, which represents the concept of the number 1, cannot be referring to any other number other than 1. If the concept of 1 changes, then it is impossible to do math. In such cases, 1 might become 2, and 2 becomes 3, and so on.

S: So I accept that numbers are immutable concepts.

T: Furthermore, numbers are also eternal concepts.

S: This is difficult for me to grasp.

T: Let us imagine the very first man who used the number 1. Let us call him Dumbo. Dumbo was the very first man who wrote the number 1 onto the walls of caves. In fact, he did that to count the number of animals he had hunted thus far. Each time he killed an animal on a hunt, he went home and wrote a “1” on the wall. He didn’t know the numerical representation of the numbers 2, 3, or even 4, but he did know how to write 1. He added the “1”s up using mental arithmetic. Obviously, the concepts or ideas of numbers 2, 3, or even 4 were known to him. If not, he wouldn’t be able to add the “1”s up.

S: So how does that explain to me that numbers are eternal concepts?

T: If Dumbo was the first man who used the number 1, does that mean that the concept or idea of 1 didn’t exist prior to the existence of Dumbo?

S: Obviously not. The concept of the number 1 seems to exist apart from the mind of Dumbo.

T: You’re right. Although the number 1 as a concept did exist in Dumbo’s mind even as he used the number 1 to calculate his kills, the number 1 was not restricted to Dumbo’s mind. Even if Dumbo’s mind was destroyed - say, eaten by a Tyrannosaurus Rex - the number 1 will continue to exist. In other words, the number 1 is a transcendent concept or idea. It exists not only outside of Dumbo’s mind, but also outside of this physical world (matter), and beyond space-time.

S: So number 1 existed prior to Dumbo?

T: Not only that. The number 1 exists outside of this world and prior to the existence of any mind in this world. More correctly, the concept of numbers exists outside of the space-time continuum.

S: So how do we know if the number 1 exists outside of this world? How do we know if the number 1 exists outside of this space-time continuum?

T: Well, if you were to destroy all minds (or all humans with minds) in this world, would the concept of number 1 continue to exist?

S: Eh, intuitively yes.

T: And if this world and this universe (or all matter) were to be destroyed, would the concept of number 1 continue to exist?

S: I believe so.

T: Or if space and time were to end now, would the concept of number 1 continue to exist?

S: Again, intuitively yes. Obviously the Big Bang didn’t “create” the concept of numbers. It seems reasonable to say that the concept of numbers existed prior to the beginning of space and time.

T: If the concept of numbers ceases to exist, mathematical logic such as "1+1 = 2" will also cease to exist.

S: Sounds reasonable to me.

T: We also recall that numbers are concepts or ideas, and can only exist in minds.

S: So if all the minds in this world are destroyed, how can the number 1 continue to exist?

T: As I had explained to you, numbers are immutable, eternal concepts that exist outside of and beyond this world, prior to the existence of minds in this world. Intuitively, you have agreed that even if all minds were to be destroyed in this world, the concept of numbers (e.g. 1, 2, 3 etc) will continue to exist, and that the concept of numbers only exists within a mind.

S: Yes, I think that even if all minds in this world were to be destroyed, the concept of numbers should continue to exist, just as math (e.g. "1+1=2") will continue to exist. But how is that possible; in what mind does the concept of numbers continue to exist?

T: If numbers are immutable, eternal concepts that exist outside of and beyond this world, and if numbers only exist in minds, it follows that numbers exist in an immutable, eternal mind that is outside of and beyond this world i.e. a transcendent mind.

S: So what is this immutable, eternal, and transcendent mind?

T: I submit to you that this is the Mind of God, an immutable, eternal mind that exists outside of and beyond this world. And numbers are concepts or ideas that exist in this Mind of God. This philosophical explanation makes the most sense when explaining the concept of numbers.

S: This is a difficult thing to grasp, but let me think about it, and I’ll get back to you tomorrow.

T: Well, if you can come up with a better explanation for the concept of numbers, do let me know. At least I have given you evidence for the existence of God - an immutable, eternal, and transcendent Being. Without the existence of this immutable, eternal, and transcendent Mind of God, one cannot explain the existence of such numerical concepts in Mathematics.

End of Scene 1

Note:

Definition of “Transcendent”: A transcendent concept or idea is not dependent upon space, time, people, or matter. For example, the concept of numbers is outside of and beyond the world, of or relating to a spiritual or nonphysical realm.

8 comments:

The highest level math class that I ever took was two semesters of Buisness Statistics for my accounting degree. The professor for that class, when we were talking about Bell curves and normal distribution, said that it had been shown that the larger the population the more data from the population you plug in the closer to a normal distribution you get. He said that you could get a normal distribution evenutally out of a population that was not normal if that population was sufficiently large enough. He asked the class "Do you realize what this mean?" One guy said "Well, yes." He said "Are you sure?" I had talked to him before and I know that his is a brother in Christ. I think his point was that since even in random stuff like a population of data that did not fit normal distribution that eventually it would become normal that proves there has to be a logic behind the numbers. It's like Paul said in Romans 1. Everything in creation testifys that there is a God.

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This is the blog of a Reformed, Evangelical Christian. I am especially interested in Christian apologetics, meta-apologetics, philosophy, and theology. I believe in engaging the culture in order to challenge its philosophical inconsistencies. It is hoped that some may see the fallacies of their world view, and come to the knowledge of the Truth in Christ Jesus.

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